4,165 research outputs found
Verification of Nondeterministic Quantum Programs
Nondeterministic choice is a useful program construct that provides a way to
describe the behaviour of a program without specifying the details of possible
implementations. It supports the stepwise refinement of programs, a method that
has proven useful in software development. Nondeterminism has also been
introduced in quantum programming, and the termination of nondeterministic
quantum programs has been extensively analysed. In this paper, we go beyond
termination analysis to investigate the verification of nondeterministic
quantum programs where properties are given by sets of hermitian operators on
the associated Hilbert space. Hoare-type logic systems for partial and total
correctness are proposed, which turn out to be both sound and relatively
complete with respect to their corresponding semantic correctness. To show the
utility of these proof systems, we analyse some quantum algorithms, such as
quantum error correction scheme, the Deutsch algorithm, and a nondeterministic
quantum walk. Finally, a proof assistant prototype is implemented to aid in the
automated reasoning of nondeterministic quantum programs.Comment: Accepted by ASPLOS '2
Verifying total correctness of graph programs
GP 2 is an experimental nondeterministic programming language based on graph transformation rules, allowing for visual programming and the solving of graph problems at a high-level of abstraction. In previous work we demonstrated how to verify graph programs using a Hoare-style proof calculus, but only partial correctness was considered. In this paper, we add new proof rules and termination functions, which allow for proofs to additionally guarantee that program executions always terminate (weak total correctness), or that programs always terminate and do so without failure (total correctness). We show that the new proof rules are sound with respect to the operational semantics of GP 2, complete for termination, and demonstrate their use on some example programs
A general theorem on the total correctness of programs in a category
AbstractIn [7], we presented a completeness theorem for proving partial correctness of programs in a large class of categories. This theorem generalized a classical result of S.Cook [5] for the language of while-programs.Here we address the total correctness of programs. Again, we use the semantics based on partially additive categories, which was introduced by M.A.Arbib and E.G.Manes [3,4,6]. Our theorems generalize the non categorical results of K.R.Apt [1,2]. They are valid for a large class of partially additive categories, including the category of sets and partial functions and the category of sets and relations, i.e. for deterministic and nondeterministic programs
Byzantine Fault Tolerance for Nondeterministic Applications
All practical applications contain some degree of nondeterminism. When such
applications are replicated to achieve Byzantine fault tolerance (BFT), their
nondeterministic operations must be controlled to ensure replica consistency.
To the best of our knowledge, only the most simplistic types of replica
nondeterminism have been dealt with. Furthermore, there lacks a systematic
approach to handling common types of nondeterminism. In this paper, we propose
a classification of common types of replica nondeterminism with respect to the
requirement of achieving Byzantine fault tolerance, and describe the design and
implementation of the core mechanisms necessary to handle such nondeterminism
within a Byzantine fault tolerance framework.Comment: To appear in the proceedings of the 3rd IEEE International Symposium
on Dependable, Autonomic and Secure Computing, 200
Automatic Probabilistic Program Verification through Random Variable Abstraction
The weakest pre-expectation calculus has been proved to be a mature theory to
analyze quantitative properties of probabilistic and nondeterministic programs.
We present an automatic method for proving quantitative linear properties on
any denumerable state space using iterative backwards fixed point calculation
in the general framework of abstract interpretation. In order to accomplish
this task we present the technique of random variable abstraction (RVA) and we
also postulate a sufficient condition to achieve exact fixed point computation
in the abstract domain. The feasibility of our approach is shown with two
examples, one obtaining the expected running time of a probabilistic program,
and the other the expected gain of a gambling strategy.
Our method works on general guarded probabilistic and nondeterministic
transition systems instead of plain pGCL programs, allowing us to easily model
a wide range of systems including distributed ones and unstructured programs.
We present the operational and weakest precondition semantics for this programs
and prove its equivalence
A Theory of Formal Synthesis via Inductive Learning
Formal synthesis is the process of generating a program satisfying a
high-level formal specification. In recent times, effective formal synthesis
methods have been proposed based on the use of inductive learning. We refer to
this class of methods that learn programs from examples as formal inductive
synthesis. In this paper, we present a theoretical framework for formal
inductive synthesis. We discuss how formal inductive synthesis differs from
traditional machine learning. We then describe oracle-guided inductive
synthesis (OGIS), a framework that captures a family of synthesizers that
operate by iteratively querying an oracle. An instance of OGIS that has had
much practical impact is counterexample-guided inductive synthesis (CEGIS). We
present a theoretical characterization of CEGIS for learning any program that
computes a recursive language. In particular, we analyze the relative power of
CEGIS variants where the types of counterexamples generated by the oracle
varies. We also consider the impact of bounded versus unbounded memory
available to the learning algorithm. In the special case where the universe of
candidate programs is finite, we relate the speed of convergence to the notion
of teaching dimension studied in machine learning theory. Altogether, the
results of the paper take a first step towards a theoretical foundation for the
emerging field of formal inductive synthesis
Fifty years of Hoare's Logic
We present a history of Hoare's logic.Comment: 79 pages. To appear in Formal Aspects of Computin
Probabilistic Rely-guarantee Calculus
Jones' rely-guarantee calculus for shared variable concurrency is extended to
include probabilistic behaviours. We use an algebraic approach which combines
and adapts probabilistic Kleene algebras with concurrent Kleene algebra.
Soundness of the algebra is shown relative to a general probabilistic event
structure semantics. The main contribution of this paper is a collection of
rely-guarantee rules built on top of that semantics. In particular, we show how
to obtain bounds on probabilities by deriving rely-guarantee rules within the
true-concurrent denotational semantics. The use of these rules is illustrated
by a detailed verification of a simple probabilistic concurrent program: a
faulty Eratosthenes sieve.Comment: Preprint submitted to TCS-QAP
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